Abstract
Chemists have long been intrigued by the molecular basis of isomerism. Indeed, much of the powerful paradigm of structure based upon the molecular graph was first invented to explain isomerism, including the classifications used in modern stereochemistry. Thus, constitutional isomers describe pairs of isomeric molecular structures possessing non-homeomorphic molecular graphs, while the classical stereoisomers (enantiomers and diastereomers) possess molecular graphs which are homeomorphic and also homeotopic (interconvertable by continuous deformation in 3-space). This means that classical stereoisomerism is derived from the Euclidean properties of molecular graphs, being a manifestation of some kind of molecular rigidity.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Frisch, H. L.; Wasserman, E. J. Am. Chem. Soc. 1961, 83, 3789–3795.
Wasserman, E. Sci. Amer. 1962, 207, 94–100.
Dietrich-Buchecker, C. O.; Sauvage, J. P. Angew. Chem. 1989, 101, 192–194.
Walba, D. M. “Stereochemical Topology,” in Chemical Applications of Topology and Graph Theory, King, R. B. (Ed.); Elsevier, Amsterdam, 1983; pp 17–32.
Walba, D. M. Tetrahedron 1985, 41, 3161–3212.
Walba, D. M. “Topological Stereochemistry: Knot Theory of Molecular Graphs,” in Graph Theory and Topology in Chemistry, King, R. B. (Ed.); Elsevier, Amsterdam, 1987; pp 23–42.
Walba, D. M.; Richards, R. M.T. Am. Chem. Soc. 1982, 104, 3219–3221.
The Möbius ladder graphs were first described in: Guy, R. K.; Harary, F. Can. Math. Bull. 1967, 10, 493–496.
Simon, J. Topology 1986, 25, 229–235.
Simon, J. “A Topological Approach to the Stereochemistry of Nonrigid Molecules,” in Graph Theory and Topology in Chemistry, King, R. B. (Ed.); Elsevier, Amsterdam, 1987; pp 43–75.
Flapan, E. “Chirality of Non-Standardly Embedded Möbius Ladders,” in Graph Theory and Topology in Chemistry, King, R. B. (Ed.); Elsevier, Amserdam, 1987; pp 76–81.
Flapan, E. Mathematische Annalen 1989, 283, 271–283.
Walba, D. M.; Simon, J.; Harary, F. Tetrahedron Lett. 1988, 29, 731–734.
Graf, E.; Lehn, J.-M. J. Am. Chem. Soc. 1975, 97, 5022–5024.
Harary, F. Graph Theory, Addison-Wesley: Reading, 1969.
Intrinsic chirality as used here was first described by Flapan in reference 7, and referred to as “inherent chirality”.
Mitchell, D. K.; Sauvage, J. P. Ange w. Chem. 1989, 100, 985–987.
Walba, D. M.; Armstrong, J. D. III; Perry, A. E.; Richards, R. M.; Homan, T. C.; Haltiwanger, R. C. Tetrahedron 1986, 42, 1883–1894.
Mislow, K. Science 1954, 120, 232.
Mislow, K.; Bolstad, R. J. Am. Chem. Soc. 1955, 77, 6712–6713.
Flapan, E. Pacific Journal of Mathematics 1987, 129, 57–66.
Eaton, P. E.; Tsanaktsidis, J. J. Am. Chem. Soc. 1990, 112, 876–878.
Hassenrück, K.; Radziszewski, J. G.; Balaji, V.; Murthy, G. S.; McKinley, A. J.; David, D. E.; Lynch, V. M.; Martin, H.-D.; Michl, J. J. Am. Chem. Soc. 1990, 112, 873–874.
Hrovat, D. A.; Borden, W, T. J. Am. Chem. Soc. 1990, 112, 875–876.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Walba, D.M. (1991). A Topological Hierarchy of Molecular Chirality and other Tidbits in Topological Stereochemistry. In: Mezey, P.G. (eds) New Developments in Molecular Chirality. Understanding Chemical Reactivity, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3698-3_4
Download citation
DOI: https://doi.org/10.1007/978-94-011-3698-3_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5644-1
Online ISBN: 978-94-011-3698-3
eBook Packages: Springer Book Archive